A splitting algorithm for system of composite monotone inclusions

TL;DR

This paper introduces a new splitting algorithm for solving systems of composite monotone inclusions in Hilbert spaces, extending previous methods and demonstrating convergence and applications to minimization problems.

Contribution

The paper presents a novel splitting algorithm for composite monotone inclusions, extending existing algorithms and proving its weak convergence.

Findings

Algorithm converges weakly in Hilbert spaces.

Applicable to minimization problems.

Extends previous splitting methods.

Abstract

We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The weak convergence of the algorithm proposed is proved. Applications to minimization problems is demonstrated.